In semiconductor devices, traps pertain to impurities or dislocations that capture carriers, and keep the carriers strongly localized. The traps play an important role in the performance and reliability of semiconductor devices. An understanding of the behaviors of the traps can improve the design, manufacture, performance and reliability of the semiconductor devices.
For example, gallium nitride (GaN) and aluminum gallium nitride (AlGaN) high-electron-mobility transistors (HEMTs) are often used in high frequency power amplifiers, high speed switches, and radar and satellite applications because of the excellent material properties of III-nitrides, such as high breakdown field, high electron mobility, high power density, and high electron saturation velocity. One requirement for high-power applications is to achieve a low resistance during and after switching ON. The dynamic ON resistance can dramatically increase with biasing conditions. These changes in ON resistance are known to be caused by a trapping effect. The exact failure mechanism of the degradation of the HEMTs is still an active area of research. Reasons for the degradation have been attributed to “hot” carriers, inverse piezoelectric effects, and lattice mismatches, for example.
Effects of the traps on the performance of the semiconductor device are temporal and eventually decay over time, i.e., the behavior of the measured quantity of the operation of the semiconductor device stabilizes and approaches a constant. Each trap is assumed to behave exponentially in time with a specific lifetime. Collectively, multiple traps influence the operation of the device. Therefore, methods that can compute and display information of the lifetimes of the trapping and detrapping processes allow detecting and analyzing the traps.
Since recovery from traps can take nano-seconds, minutes, or even days, the analysis of this effect is extremely important because traps severely degrade the performance and reliability of semiconductor devices. Trap analysis is also important for characterizing the formation and behavior of traps so that the devices can be modeled, designed, and manufactured with improved performance and reliability. The lifetimes can be related to the temperatures and activation energies of the traps. The captured or released coefficient could be a function of the initial number of traps to be filled or number of carriers in the traps to be released, respectively.
The information of the lifetimes of the traps, as a function of temperature, allows one to calculate the activation energy and cross-sectional density of the traps, which are very important parameters to understand the behavior of traps. Current GaN device electrical models do not capture the characteristics of traps. Accurate extraction of trap lifetimes of a device would provide information that leads to development of more accurate electrical models of the device. System design using the device with a more accurate device model, such as the design of a RF power amplifier, would greatly help to achieve optimal performance, such as power efficiency and distortion reduction.
Conventional methods for analyzing trap behavior in GaN HEMTs include a method described by Jungwoo et al., “A Current-Transient Methodology for Trap Analysis for GaN High Electron Mobility Transistors,” IEEE Transactions on, 58(1):132-140, 2011, and a method described by Donghyun et al., “Mechanisms responsible for dynamic ON-resistance in GaN high-voltage HEMTs,” Power Semiconductor Devices and ICs (ISPSD), 2012 24th International Symposium on, pages 333-336, 2012. Those conventional methods are inaccurate and computationally complex.
The above conventional methods are based on the least square fitting using basis functions, which are non-orthogonal to each other, with a uniform, in the logarithmic time scale, placement of the time constants describing trap lifetimes, essentially assuming a continuous distribution of trap lifetimes. A good fitting requires the number of the basis functions to be large enough, in which case the basis functions in the prior art are not just non-orthogonal, but also nearly linearly dependent. A numerically valid basis is not formed in those conventional methods, leading to an extremely poorly conditioned least squares problem and thus resulting in erroneous lifetime computations. Conventional approaches apply constraints, such as lower and upper bounds or smoothness in the spectrum, in the least square fitting, to decrease the ill-conditioning, but this dramatically increases the computational time, while still not resolving satisfactory the inaccuracy in the lifetime calculations.
Accordingly, there is a need to provide an efficient and accurate method for analyzing traps in the semiconductor devices.